Improved Approximation Algorithms for Metric Max TSP

  • Zhi-Zhong Chen
  • Takayuki Nagoya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

We present two polynomial-time approximation algorithms for the metric case of the maximum traveling salesman problem. One of them is for directed graphs and its approximation ratio is \(\frac{27}{35}\). The other is for undirected graphs and its approximation ratio is \(\frac{7}{8} - o(1)\). Both algorithms improve on the previous bests.

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References

  1. 1.
    Barvinok, A.I., Johnson, D.S., Woeginger, G.J., Woodroofe, R.: Finding Maximum Length Tours under Polyhedral Norms. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds.) IPCO 1998. LNCS, vol. 1412, pp. 195–201. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  2. 2.
    Chen, Z.-Z., Okamoto, Y., Wang, L.: Improved Deterministic Approximation Algorithms for Max TSP. To appear in Information Processing LettersGoogle Scholar
  3. 3.
    Hassin, R., Rubinstein, S.: A 7/8-Approximation Approximations for Metric Max TSP. Information Processing Letters 81, 247–251 (2002)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kaplan, H., Lewenstein, M., Shafrir, N., Sviridenko, M.: Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular Multigraphs. In: Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, pp. 56–75 (2003)Google Scholar
  5. 5.
    Kostochka, A.V., Serdyukov, A.I.: Polynomial Algorithms with the Estimates \(\frac{3}{4}\) and \(\frac{5}{6}\) for the Traveling Salesman Problem of Maximum (in Russian). Upravlyaemye Sistemy 26, 55–59 (1985)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Zhi-Zhong Chen
    • 1
  • Takayuki Nagoya
    • 1
  1. 1.Dept. of Math. Sci.Tokyo Denki Univ.Hatoyama, SaitamaJapan

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